Podcast
Questions and Answers
What is the basic idea of time series data?
What is the basic idea of time series data?
- Time series data are collected on different observational units at a single time period
- Time series data are collected on different observational units at multiple time periods
- Time series data are collected on the same observational unit at a single time period
- Time series data are collected on the same observational unit at multiple time periods (correct)
What are time series models often not based on?
What are time series models often not based on?
- Historical data
- Statistical models
- Experimental data
- Theoretical economic models (correct)
What are time series models usually indexed with?
What are time series models usually indexed with?
- i, index
- p, period
- d, date
- t, time (correct)
What is the formal definition of a white noise process?
What is the formal definition of a white noise process?
What is the null hypothesis in the Ljung-Box Q-test for autocorrelation?
What is the null hypothesis in the Ljung-Box Q-test for autocorrelation?
What does the autocorrelation function (ACF) indicate about the stationarity of a time series?
What does the autocorrelation function (ACF) indicate about the stationarity of a time series?
What is the best forecast for $y_{t+1}$ in a white noise process with constant mean?
What is the best forecast for $y_{t+1}$ in a white noise process with constant mean?
What is the conventional definition used for time series data when calculating the autocorrelation function?
What is the conventional definition used for time series data when calculating the autocorrelation function?
What does the ACF computation assume about the process?
What does the ACF computation assume about the process?
What information does the ACF provide for nonstationary series?
What information does the ACF provide for nonstationary series?
What is the implication of positive autocorrelation in a time series?
What is the implication of positive autocorrelation in a time series?
Which concept is commonly referred to in the literature when discussing stationarity in time series analysis?
Which concept is commonly referred to in the literature when discussing stationarity in time series analysis?
What is a key reason for using natural logs in time series analysis?
What is a key reason for using natural logs in time series analysis?
What is the primary focus of macroeconometrics?
What is the primary focus of macroeconometrics?
What is the purpose of using time series data in economic analysis?
What is the purpose of using time series data in economic analysis?
In what form have the Real vs. nominal housing price indices for the Helsinki Metro Area been observed?
In what form have the Real vs. nominal housing price indices for the Helsinki Metro Area been observed?
What is a technical issue raised by time series data in economic analysis?
What is a technical issue raised by time series data in economic analysis?
What is the focus of macroeconomists when using time series data?
What is the focus of macroeconomists when using time series data?
What is a persistent, long-term movement or tendency in the data called?
What is a persistent, long-term movement or tendency in the data called?
Which type of time series becomes stationary after removing a deterministic trend from it?
Which type of time series becomes stationary after removing a deterministic trend from it?
What is a stochastic trend with serially uncorrelated disturbances called?
What is a stochastic trend with serially uncorrelated disturbances called?
What is the correlation of a series with its own lagged values called?
What is the correlation of a series with its own lagged values called?
What type of time series are called I(0)?
What type of time series are called I(0)?
What type of time series are called I(1)?
What type of time series are called I(1)?
What type of time series are called I(2)?
What type of time series are called I(2)?
What is a nonrandom function of time called?
What is a nonrandom function of time called?
What is a random and varies over time called?
What is a random and varies over time called?
What should be used for regression analysis if a time series has a random walk trend?
What should be used for regression analysis if a time series has a random walk trend?
What are estimates of the population autocorrelations computed over observations in the time series called?
What are estimates of the population autocorrelations computed over observations in the time series called?
What is the correlation of a series with its own lagged values called?
What is the correlation of a series with its own lagged values called?
In the context of time series modelling, what is the primary assumption underlying the AR(p) model?
In the context of time series modelling, what is the primary assumption underlying the AR(p) model?
What type of time series memory is associated with the long-term effect of a shock gradually disappearing over time?
What type of time series memory is associated with the long-term effect of a shock gradually disappearing over time?
What is the distinguishing feature of short-term memory in time series processes?
What is the distinguishing feature of short-term memory in time series processes?
What is the Box-Jenkins estimation approach primarily focused on?
What is the Box-Jenkins estimation approach primarily focused on?
What does the Yule-Walker equations solve for in an AR model?
What does the Yule-Walker equations solve for in an AR model?
In an AR model, what is the implication of a negative coefficient?
In an AR model, what is the implication of a negative coefficient?
What condition makes an AR model stationary?
What condition makes an AR model stationary?
What does the reaction to a shock in an AR model depend on?
What does the reaction to a shock in an AR model depend on?
What do non-stationary AR processes lead to?
What do non-stationary AR processes lead to?
What do the partial autocorrelation function measure in an AR model?
What do the partial autocorrelation function measure in an AR model?
What is the primary focus of an AR(p) model?
What is the primary focus of an AR(p) model?
What influences the behavior of the series in an AR model?
What influences the behavior of the series in an AR model?
What does a greater coefficient in an AR model imply?
What does a greater coefficient in an AR model imply?
What can capture seasonal variation in yt in an AR model?
What can capture seasonal variation in yt in an AR model?
What is the predicted value of yt calculated using in a simple AR(1) model?
What is the predicted value of yt calculated using in a simple AR(1) model?
What can be used to solve for the autocorrelations and AR coefficients in an AR model?
What can be used to solve for the autocorrelations and AR coefficients in an AR model?
What is commonly used for model selection in econometric modeling?
What is commonly used for model selection in econometric modeling?
What is the implication of non-normality of the error term in econometric modeling?
What is the implication of non-normality of the error term in econometric modeling?
What is the main focus of diagnostic checks in econometric modeling?
What is the main focus of diagnostic checks in econometric modeling?
What is the primary consideration for selecting the best model in econometric modeling?
What is the primary consideration for selecting the best model in econometric modeling?
What is the recommended approach to controlling non-normality of the error term in econometric modeling?
What is the recommended approach to controlling non-normality of the error term in econometric modeling?
What is the purpose of comparing models using the same sample period and fixed T in econometric modeling?
What is the purpose of comparing models using the same sample period and fixed T in econometric modeling?
What is the primary focus of maximum likelihood estimation in econometric modeling?
What is the primary focus of maximum likelihood estimation in econometric modeling?
What is the reason for not recommending overdifferencing in econometric modeling?
What is the reason for not recommending overdifferencing in econometric modeling?
What is the primary consideration for selecting parsimonious models in econometric modeling?
What is the primary consideration for selecting parsimonious models in econometric modeling?
What is the focus of formal testing such as the Jarque-Bera test in econometric modeling?
What is the focus of formal testing such as the Jarque-Bera test in econometric modeling?
Why is testing for autocorrelation particularly important in econometric modeling?
Why is testing for autocorrelation particularly important in econometric modeling?
What is the primary purpose of visual inspection in econometric modeling?
What is the primary purpose of visual inspection in econometric modeling?
What is the distinguishing feature of an autoregressive model (AR(p))?
What is the distinguishing feature of an autoregressive model (AR(p))?
Which type of time series memory is associated with the long-term effect of a shock gradually disappearing over time?
Which type of time series memory is associated with the long-term effect of a shock gradually disappearing over time?
What is the primary focus of the Box-Jenkins estimation approach mentioned in the handout?
What is the primary focus of the Box-Jenkins estimation approach mentioned in the handout?
What type of time series modelling is based on the assumption that the market immediately corrects itself after a shock?
What type of time series modelling is based on the assumption that the market immediately corrects itself after a shock?
Which method is commonly used for estimation in the identification stage of econometric modeling?
Which method is commonly used for estimation in the identification stage of econometric modeling?
What is the purpose of diagnostic checks in econometric modeling?
What is the purpose of diagnostic checks in econometric modeling?
Which information criteria are commonly used for model selection in econometric modeling?
Which information criteria are commonly used for model selection in econometric modeling?
What do non-normality of the error term lead to in econometric modeling?
What do non-normality of the error term lead to in econometric modeling?
What do diagnostic checks in econometric modeling aim to detect?
What do diagnostic checks in econometric modeling aim to detect?
What is the implication of residual autocorrelation in a time series model?
What is the implication of residual autocorrelation in a time series model?
What is the primary focus of comparing models using the same sample period and fixed T in econometric modeling?
What is the primary focus of comparing models using the same sample period and fixed T in econometric modeling?
What is the primary focus of formal testing such as the Jarque-Bera test in econometric modeling?
What is the primary focus of formal testing such as the Jarque-Bera test in econometric modeling?
What is the purpose of using point dummy variables or the Student's t-distribution in econometric modeling?
What is the purpose of using point dummy variables or the Student's t-distribution in econometric modeling?
What is the conventional approach for model comparison in econometric modeling?
What is the conventional approach for model comparison in econometric modeling?
What is the primary assumption underlying the AR(p) model in time series modeling?
What is the primary assumption underlying the AR(p) model in time series modeling?
What is the implication of positive autocorrelation in a time series?
What is the implication of positive autocorrelation in a time series?
What is the implication of residual autocorrelation in a time series model?
What is the implication of residual autocorrelation in a time series model?
What do non-stationary AR processes lead to?
What do non-stationary AR processes lead to?
What are the Yule-Walker equations used to solve for in an AR model?
What are the Yule-Walker equations used to solve for in an AR model?
What is the primary focus of the Box-Jenkins estimation approach mentioned in the handout?
What is the primary focus of the Box-Jenkins estimation approach mentioned in the handout?
What is the primary purpose of using time series data in economic analysis?
What is the primary purpose of using time series data in economic analysis?
What is the primary focus of diagnostic checks in econometric modeling?
What is the primary focus of diagnostic checks in econometric modeling?
What is the connection between AR(1) and MA(∞) models through mathematical presentation?
What is the connection between AR(1) and MA(∞) models through mathematical presentation?
What is the definition of an ARMA(p,q) model?
What is the definition of an ARMA(p,q) model?
What is the primary focus of an ARIMA(p,d,q) process/model?
What is the primary focus of an ARIMA(p,d,q) process/model?
What is the Box-Jenkins procedure for estimating ARMA models primarily focused on?
What is the Box-Jenkins procedure for estimating ARMA models primarily focused on?
What is the difficulty in distinguishing between similar ARMA models primarily attributed to?
What is the difficulty in distinguishing between similar ARMA models primarily attributed to?
What is the primary purpose of the ARCH-test in time series analysis?
What is the primary purpose of the ARCH-test in time series analysis?
What is the implication of heteroscedasticity on the estimated parameters in time series modeling?
What is the implication of heteroscedasticity on the estimated parameters in time series modeling?
What is the purpose of the Newey-West HAC estimator in econometric modeling?
What is the purpose of the Newey-West HAC estimator in econometric modeling?
What is the primary focus of the Chow Breakpoint test in time series analysis?
What is the primary focus of the Chow Breakpoint test in time series analysis?
What is the implication of rejecting the null hypothesis in the ARCH-test?
What is the implication of rejecting the null hypothesis in the ARCH-test?
What does the Newey-West HAC estimator provide in the presence of autocorrelation and heteroscedasticity?
What does the Newey-West HAC estimator provide in the presence of autocorrelation and heteroscedasticity?
What is the implication of clustered or autocorrelated volatility in a time series?
What is the implication of clustered or autocorrelated volatility in a time series?
What is the primary purpose of the Q-test in time series analysis?
What is the primary purpose of the Q-test in time series analysis?
What is the primary implication of rejecting the hypothesis of no autocorrelation in squared residuals?
What is the primary implication of rejecting the hypothesis of no autocorrelation in squared residuals?
What is the primary condition for the baseline IGARCH model to have a stationary variance?
What is the primary condition for the baseline IGARCH model to have a stationary variance?
What is the distinguishing feature of the EGARCH model proposed by Nelson (1991)?
What is the distinguishing feature of the EGARCH model proposed by Nelson (1991)?
What is the additional feature of the TARCH (GJR-GARCH) model proposed by Zakoian (1994) and Glosten et al. (1993)?
What is the additional feature of the TARCH (GJR-GARCH) model proposed by Zakoian (1994) and Glosten et al. (1993)?
What is the primary feature of the APARCH model proposed by Ding, Engle & Granger (1993)?
What is the primary feature of the APARCH model proposed by Ding, Engle & Granger (1993)?
What is the primary difference between ARCH and GARCH models?
What is the primary difference between ARCH and GARCH models?
What is the key contribution of Robert Engle, the winner of the 2003 Nobel Memorial Prize in Economic Sciences, to volatility modeling?
What is the key contribution of Robert Engle, the winner of the 2003 Nobel Memorial Prize in Economic Sciences, to volatility modeling?
What is the primary focus of the ARCH-test in time series analysis?
What is the primary focus of the ARCH-test in time series analysis?
What is the significance of clustered volatility in financial market research?
What is the significance of clustered volatility in financial market research?
What is the main reason for the substantial interest in volatility modeling in financial market research since the 1980s?
What is the main reason for the substantial interest in volatility modeling in financial market research since the 1980s?
What did Robert Engle's work demonstrate regarding the estimation of time series?
What did Robert Engle's work demonstrate regarding the estimation of time series?
What is the key concept underlying GARCH models in volatility modeling?
What is the key concept underlying GARCH models in volatility modeling?
What is the primary focus of Eviews UG II, Chapter 25 mentioned in the handout?
What is the primary focus of Eviews UG II, Chapter 25 mentioned in the handout?
What is the preferred ARMA model for returns based on AIC & SC?
What is the preferred ARMA model for returns based on AIC & SC?
What type of residuals should not exhibit autocorrelation in a well-specified GARCH model?
What type of residuals should not exhibit autocorrelation in a well-specified GARCH model?
What type of estimation is required for correct standard errors of coefficients when dealing with non-normally distributed residuals?
What type of estimation is required for correct standard errors of coefficients when dealing with non-normally distributed residuals?
What type of model successfully captures conditional volatility with homoskedastic residuals?
What type of model successfully captures conditional volatility with homoskedastic residuals?
What type of graph is used for the ARIMA(1,1,0)-GARCH(1,1) model for OMX Helsinki Small Cap index?
What type of graph is used for the ARIMA(1,1,0)-GARCH(1,1) model for OMX Helsinki Small Cap index?
What is the purpose of using dummy variables in testing effects on conditional volatility?
What is the purpose of using dummy variables in testing effects on conditional volatility?
What does the GARCH-in-Mean model link to conditional variance?
What does the GARCH-in-Mean model link to conditional variance?
What type of test indicates heteroscedasticity, prompting continuation with GARCH modeling?
What type of test indicates heteroscedasticity, prompting continuation with GARCH modeling?
What type of residuals are required for correct standard errors of coefficients in econometric modeling?
What type of residuals are required for correct standard errors of coefficients in econometric modeling?
What type of model is preferred over ARMA(2,3) based on AIC & SC?
What type of model is preferred over ARMA(2,3) based on AIC & SC?
What type of residuals should not exhibit autocorrelation in a well-specified model?
What type of residuals should not exhibit autocorrelation in a well-specified model?
What type of model successfully captures conditional volatility with homoskedastic residuals?
What type of model successfully captures conditional volatility with homoskedastic residuals?
Flashcards
Macroeconometrics
Macroeconometrics
Macroeconometrics focuses on forecasting models for economic variables like GDP, inflation, and interest rates, considering their limitations and the complexity of factors influencing these variables.
Time series data
Time series data
Time series data is a sequence of observations taken at regular intervals over time, allowing for analysis of trends, patterns and relationships within the data.
Nominal GDP
Nominal GDP
Nominal GDP is the value of goods and services produced in a country at current market prices, without adjusting for inflation.
Real GDP
Real GDP
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Seasonally adjusted data
Seasonally adjusted data
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Private sector credit to GDP ratio
Private sector credit to GDP ratio
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Inflation rate
Inflation rate
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Natural log transformation
Natural log transformation
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Stationary time series
Stationary time series
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Non-stationary time series
Non-stationary time series
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Integrated order (I(0) and I(1))
Integrated order (I(0) and I(1))
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Trend
Trend
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Deterministic vs. Stochastic trend
Deterministic vs. Stochastic trend
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Random walk
Random walk
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Autocorrelation
Autocorrelation
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Sample autocorrelations
Sample autocorrelations
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Identification stage
Identification stage
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Maximum Likelihood estimation
Maximum Likelihood estimation
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Overdifferencing
Overdifferencing
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Parsimony
Parsimony
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Information criteria
Information criteria
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Out-of-sample forecast accuracy
Out-of-sample forecast accuracy
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Diagnostic Checks
Diagnostic Checks
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White noise
White noise
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Testing for autocorrelation
Testing for autocorrelation
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Residual normality
Residual normality
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MA(q) process
MA(q) process
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ARMA(p,q) model
ARMA(p,q) model
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ARIMA(p,d,q) model
ARIMA(p,d,q) model
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GARCH(p,q) model
GARCH(p,q) model
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GARCH-in-Mean (GARCH-M) model
GARCH-in-Mean (GARCH-M) model
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Study Notes
Macroeconometrics and Time Series Data
- Macroeconometrics focuses on forecasting models and their limitations, such as the difficulty of including quarterly GDP changes in daily stock return forecasts.
- Macroeconomists use extensive time series data on economic fundamentals like GDP, consumption, household indebtedness, inflation, and interest rates, which can be observed in real or nominal terms and seasonally adjusted or not.
- Nominal GDP for Finland has been observed quarterly from 1975Q1 to 2023Q2, with 194 observations.
- Finland's private sector credit to GDP ratio has been observed quarterly from 1970Q1 to 2023Q1, with 213 observations.
- The inflation rate in Finland, based on changes in the consumer price index, has been observed from 2000Q1 to 2020Q2, with notable seasonal variation.
- Real vs. nominal housing price indices for the Helsinki Metro Area have been observed in natural log form from 1975Q1 to 2020Q2.
- The S&P 500 Total Return Index has been observed daily from 11.9.1989 to 11.9.2020, with 7817 daily observations and a natural log transformed index.
- Neste Share Return in Helsinki Stock Exchange has been observed for daily returns from 18.4.2005 to 11.9.2020.
- Time series data is used for forecasting, estimating dynamic causal effects, modeling risks, and testing economic theories, with applications in various fields including environmental modeling and computer science.
- Time series data raises technical issues such as time lags, correlation over time, calculation of standard errors for serially correlated errors, and data stationarity.
- Natural logs are used in time series analysis for various reasons, including closer approximation to normal distribution and better reflecting long-term mean returns.
- Stationarity is a key assumption in time series analysis, with the concept of covariance stationarity or weak stationarity being commonly referred to in the literature.
Time Series Analysis and Stationarity
- Time series analysis involves verifying whether the time series is stationary or non-stationary
- Conventional estimation techniques and testing procedures do not generally apply for non-stationary time series
- Stationary time series are called I(0), while difference stationary time series are called I(1)
- Some variables need to be differenced twice in order to get stationary series, and are called I(2)
- Trend stationary time series becomes stationary after removing a deterministic trend from it
- A trend is a persistent, long-term movement or tendency in the data
- Deterministic trend is a nonrandom function of time, while a stochastic trend is random and varies over time
- A random walk is a stochastic trend with serially uncorrelated disturbances
- If a time series has a random walk trend, then ΔYt is stationary and regression analysis should be undertaken using ΔYt instead of Yt
- Stock return index value can be a random walk with drift, a stochastic trend, which is difference stationary (I(1))
- Autocorrelation or serial correlation is the correlation of a series with its own lagged values
- Sample autocorrelations are estimates of the population autocorrelations, and are computed over observations in the time series.
Econometric Model Selection and Diagnostic Checks
- In the identification stage, several alternative models are suggested for estimation.
- Maximum Likelihood estimation is commonly applied in the estimation stage.
- Overdifferencing is not recommended as valuable information is lost.
- The selection of the best model considers the parsimony, statistical significance, model fit, information criteria, out-of-sample forecast accuracy, and diagnostic checks.
- Parsimonious models typically produce more accurate forecasts and should generally have statistically significant parameters.
- Information criteria such as Akaike and Schwartz are commonly used for model selection.
- Comparing models using the same sample period and fixed T in the estimations is essential.
- Diagnostic checks aim to detect whether the model reflects the DGP well and if the error term is white noise.
- Visual inspection and formal tests are used to check for outlier observations, structural changes, autocorrelation, and residual normality.
- Testing for autocorrelation is particularly important as evidence of residual autocorrelation implies that the model does not cater for some systematic process in the time series.
- Residual normality is often assumed, and formal testing such as the Jarque-Bera test is applied.
- Non-normality of the error term can lead to unreliable confidence intervals and p-values, and can be controlled using point dummy variables or the Student's t-distribution.
Econometric Model Selection and Diagnostic Checks
- In the identification stage, several alternative models are suggested for estimation.
- Maximum Likelihood estimation is commonly applied in the estimation stage.
- Overdifferencing is not recommended as valuable information is lost.
- The selection of the best model considers the parsimony, statistical significance, model fit, information criteria, out-of-sample forecast accuracy, and diagnostic checks.
- Parsimonious models typically produce more accurate forecasts and should generally have statistically significant parameters.
- Information criteria such as Akaike and Schwartz are commonly used for model selection.
- Comparing models using the same sample period and fixed T in the estimations is essential.
- Diagnostic checks aim to detect whether the model reflects the DGP well and if the error term is white noise.
- Visual inspection and formal tests are used to check for outlier observations, structural changes, autocorrelation, and residual normality.
- Testing for autocorrelation is particularly important as evidence of residual autocorrelation implies that the model does not cater for some systematic process in the time series.
- Residual normality is often assumed, and formal testing such as the Jarque-Bera test is applied.
- Non-normality of the error term can lead to unreliable confidence intervals and p-values, and can be controlled using point dummy variables or the Student's t-distribution.
Time Series Analysis and ARMA Models
- MA(1) process examples with different parameters and autocorrelation values
- Example of MA(2) process with parameters and autocorrelation value based on true data
- Mean and variance equations for MA(1) and MA(q) processes
- Explanation of autocorrelation in MA(q) process and its drop to zero after q lags
- Theoretical ACF and PACF for MA(1) process and its application to real-life data
- Connection between AR(1) and MA(∞) models through mathematical presentation
- Explanation of ARMA(p,q) model as a combination of AR(p) and MA(q) models
- Difficulty in distinguishing between similar ARMA models and the influence of lag length on data frequency
- Definition and components of ARIMA(p,d,q) process/model
- Difficulty in identifying correct p and q for ARMA process and starting estimation with ARMA(1,1) model
- Inclusion of other explanatory variables in ARIMA model and discussion on seasonal variation
- Box-Jenkins procedure for estimating ARMA models, including identification and estimation steps, and the goal of finding a parsimonious model that reflects the DGP and produces white noise error terms
Estimating GARCH Models and GARCH-in-Mean Models
- ARMA(2,|3|) for returns, based on Box-Jenkins procedure, but not normally distributed error term with fat tails, potentially due to heteroscedasticity
- Addition of Covid19 dummy has minimal impact on model
- Both Q-test and ARCH test indicate heteroscedasticity, prompting continuation with GARCH modeling
- Preference for AR(1) over ARMA(2,|3|) based on AIC & SC, resulting in AR(1)-GARCH(1,1) model
- Standardized residuals Zt should not exhibit autocorrelation, ensuring well-specified model
- Non-normally distributed Zt requires QML estimation for correct std. errors of coefficients
- GARCH(1,1) model successfully captures conditional volatility with homoskedastic residuals
- Non-normal residuals after QML estimation, but coefficients remain statistically highly significant
- Conditional standard deviation (ℎ𝑡) graphed for ARIMA (1,1,0)-GARCH(1,1) model for OMX Helsinki Small Cap index
- Use of dummy variables to test effects on conditional volatility (e.g., Covid19) considered
- Unconditional vs. conditional mean and variance concepts explained in the context of GARCH models
- Introduction and explanation of GARCH-in-Mean model, which links risk premium to conditional variance
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